MU2 PILOT REPORTS FAILURE OF FUEL TO TRANSFER FROM TIP TANKS AND MISSED APPROACH DUE TO WEATHER. PILOT RECEIVES LOW ALTITUDE WARNING FROM ATC DURING APPROACH AND GETS IMMEDIATE VECTORS TO ZZZ DUE TO LOW FUEL AFTER MISSED APPROACH.

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I WAS SCHEDULED TO FLY A REPO FLT TO HWD. I CHKED THE WX AT HWD AND IT WAS ABOVE LNDG MINIMUMS FOR THE APCH TO BE USED. WHILE IN CRUISE FLT; I NOTICED SEVERAL ISSUES WITH THE ACFT. FIRST; THE FUEL WAS NOT XFERRING FROM THE TIPS TO THE MAINS. IT WASN'T THE CAPS BECAUSE I PUT THEM ON PERSONALLY AFTER BEING REFUELED. SECOND; THE XPONDER REPLY LIGHT WASN'T ILLUMINATING AND THE UNIT WAS GIVING INCORRECT READINGS TO ATC. I SWITCHED TO THE STANDBY XPONDER AND ALL SEEMED FINE FOR THE MOMENT. AS I APCHED HWD; I NOTICED THERE WAS OVER 1000 LBS OF FUEL IN THE TIPS I COULDN'T USE. ON TOP OF THAT; HWD WAS BELOW LNDG MINIMUMS. THE FOG LOOKED WIDESPREAD SO AGAINST MY BETTER JUDGEMENT I CHOSE TO TRY AND SHOOT THE APCH BECAUSE I COULD JUST MAKE OUT THE END OF THE RWY THROUGH A CLEARING IN THE FOG. I STARTED THE APCH AND NORCAL SHIPPED ME TO TWR. THEN THE DME STARTED GIVING ERRATIC DISPLAYS OF DISTANCE. TWR THEN ADVISED ME OF A LOW ALT ALERT. I WAS STILL IN VMC ON TOP OF THE FOG. THEN THE DME CAME BACK UP AND I CONTINUED THE APCH. I WENT DOWN TO MINIMUMS AND WENT MISSED. ON CLBOUT; I CONTACTED NORCAL AND TOLD THEM MY SITUATION ABOUT FUEL AND NEEDING A VMC/ABOVE LNDG MINIMUM ARPT. NORCAL THEN VECTORED A B737 AROUND ME. I THINK IT IS POSSIBLE MY XPONDER WAS GIVING BAD ALT READOUTS. ATC HELPED ME FIND ZZZ; I THANKED THEM; LANDED AND FUELED. ONCE HWD WENT BACK TO VMC; I DEPARTED. ZZZ TWR THEN ADVISED ME OF SMOKING ENGS. I SUSPECT IT WAS FUEL. I LANDED BACK AT HWD WITHOUT ADDITIONAL PROBS. ONCE I ARRIVED; I CONTACTED MAINT ABOUT THE ISSUES I HAD AND MADE SURE THEY APPRECIATED THE SERIOUSNESS OF THE SITUATION. THE ACFT WAS EVENTUALLY FIXED AND RETURNED TO SVC. I BELIEVE THAT THIS INCIDENT HAPPENED BECAUSE OF POOR DECISION MAKING AND POOR PLANNING. HAD I JUST ADVISED ATC ORIGINALLY OF MY FUEL SITUATION AND DIVERTED; THIS EVENT WOULD NOT HAVE SNOWBALLED OUT OF CONTROL LIKE IT DID. IN THE FUTURE; I MUST PUT SAFETY FIRST AND WEIGH THE RISKS ASSOCIATED WITH CERTAIN DECISIONS. IN THE END; I ENDED UP EXACTLY WHERE I WOULD HAVE IF I HAD DIVERTED IN THE FIRST PLACE AT ZZZ. WHY PUT YOURSELF THROUGH SO MUCH ADDED STRESS BY HAVING 'GET THEREITIS.' I FOR ONE WILL NOT -- NO MATTER HOW IMPORTANT THE FLT IS.